One thing that one of our guys thought that might be a factor in the equation was FastCGI, but this was not proven conclusively. It is worth looking at since logically it could be a factor. Other things to consider could be PHP configuration settings, Zend, PHP version, other server side stuff.
Another approach that may work is to use the WP Super Cache manual page cache creation tools and then do not expire the cache/set an expiration date and do not use the garbage collection timer. By doing that you will have good cached pages. You would then manually delete or create cache at later times. In other words, do not use any WP Super Cache automation and instead control everything manually.